Method and apparatus for estimation of orthogonal frequency division multiplexing symbol timing and carrier frequency offset

ABSTRACT

A system and method estimates symbol timing of long training symbols and coarse carrier frequency offset in an orthogonal frequency division multiplexing receiver of a wireless local area network. The system and method estimates the symbol timing and coarse carrier frequency offset during short training symbols of a preamble of a data packet. Fine carrier frequency offset is estimated during long training symbols. Channel estimates during a data portion of the data packet are adapted.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/273,487, filed Mar. 5, 2001, which is hereby incorporated byreference.

FIELD OF THE INVENTION

The present invention relates to receivers, and more particularly toreceivers that measure carrier frequency offset, symbol timing and/orphase noise of an orthogonal frequency division multiplexing signal.

BACKGROUND OF THE INVENTION

A wireless local area network (WLAN) uses radio frequency (RF) signalsto transmit and receive data between electronic devices. WLANs provideall of the features and benefits of traditional hard-wired LANs withoutrequiring cable connections between the devices. In WLANs, transmittersand receivers (often implemented as wireless network interface cards)provide a wireless interface between a client and a wireless accesspoint to create a transparent connection between the client and thenetwork. Alternately, the WLAN provides a wireless interface directlybetween two devices.

The access point is the wireless equivalent of a hub. The access pointis typically connected to the WLAN backbone through a standard Ethernetcable and communicates with the wireless devices using an antenna. Thewireless access point maintains the connections to clients that arelocated in a coverage area of the access point. The wireless accesspoint also typically handles security by granting or denying access.

IEEE section 802.11(a), which is hereby incorporated by reference,standardized WLANs that operate at approximately 5 GHz with data speedsup to 54 Mbps. A low band operates at frequencies from 5.15 to 5.25 GHzwith a maximum power output of 50 mW. A middle band operates atfrequencies from 5.25 to 5.35 GHz with a maximum power output of 250 mW.A high band operates at frequencies from 5.75 to 5.85 GHz with a maximumpower output of 1000 mW.

Because of the high power output, wireless devices operating in the highband will tend to include building-to-building and outdoor applications.The low and middle bands are more suitable for in-building applications.IEEE section 802.11(a) employs orthogonal frequency divisionmultiplexing (OFDM) instead of direct sequence spread spectrum (DSSS)that is employed by IEEE section 802.11(b). OFDM provides higher datarates and reduces transmission echo and distortion that are caused bymultipath propagation and radio frequency interference (RFI).

Referring now to FIG. 1, data packets include a preamble 10 that isspecified by IEEE section 802.11(a). The preamble 10 includes aplurality of short training symbols 12 (S0, . . . , S9). The shorttraining symbols 12 are followed by a guard interval 14 (Guard) and twolong training symbols 16-1 and 16-2 (L0, L1). The duration of the shorttraining symbol 12 is T_(short), the duration of the guard interval 14is T_(G12), the duration of the long training symbols 16 is T_(long),the duration of the guard interval 15 for data symbols is T_(G1), andthe duration of data symbols 18 is T_(data). Guard intervals 15 and datasymbols 18 alternate after the long training symbols 16. According toIEEE section 802.11(a), T_(short)=0.8 μs, T_(G1)=0.8 μs, T_(G12)=1.6 μs,T_(long)=3.2 μs, and T_(data)=4 μs.

One important task of the OFDM receiver is the estimation of symboltiming and carrier frequency offset. Symbol timing is needed todetermine the samples of each OFDM symbol that correspond to the guardinterval and the samples that are used for fast Fourier transform (FFT)processing. Compensation of the carrier frequency offset is also neededto maximize signal amplitude and minimize inter-carrier interference(ICI).

Conventional symbol timing circuits correlate two halves of a singleOFDM training symbol whose duration is equal to the duration of the datasymbols. For example, see the symbol timing circuit disclosed in T.Schmidl and D.C. Cox, “Robust Frequency and Timing Synchronization forOFDM”, IEEE Trans. Commun., vol. 45, no. 12, (December 1999), pp.1613–1621, which is hereby incorporated by reference. The conventionalsymbol timing circuit exhibits a plateau when there is no intersymbolinterference (ISI). The duration of the plateau is the duration of theguard interval that is not affected by ISI. The plateau in theconventional symbol timing circuit corresponds to the range ofacceptable times for the start of the frame. For example, the center ofthe plateau is a desirable estimate of the symbol timing. Since only onetraining symbol is employed, the conventional symbol timing circuit doesnot allow time for possible switching of antennas and corresponding AGCsettling during packet detection.

SUMMARY OF THE INVENTION

A system and method according to the invention estimates carrierfrequency offset in an orthogonal frequency division multiplexingreceiver of a wireless local area network. Short training symbols of apreamble of a data packet are sampled to generate a received signal.Sign bits of real and imaginary components of the received signal arequantized.

In other features, the sign bits of at least two adjacent short trainingsymbols are used to generate a correlation signal. A filtered sum of anabsolute value of a real component of the correlation signal and anabsolute value of an imaginary component of the correlation signal aregenerated.

In still other features, a local maximum value of the filtered sum isidentified during the short training symbols. The local maximum value isidentified by updating and storing the filtered sums and by comparing atleast one filtered sum to a prior filtered sum and to a subsequentfiltered sum.

In still other features, the local maximum value of the filtered sum ismultiplied by a threshold value to identify a right edge of a plateau. Aright time index value corresponding to the right edge is identified.Symbol timing of long training symbols is calculated from the right timeindex value.

In still other features, a maximum value of the filtered sum isidentified during the short training symbols. The maximum value isidentified by updating and storing the filtered sums and by comparing atleast one filtered sum to a prior filtered sum and to a subsequentfiltered sum. A time index value corresponding to the maximum value isidentified. A correlation signal value corresponding to the time indexvalue is identified. An imaginary component of the correlation signalvalue corresponding to the time index value is calculated. A realcomponent of the correlation signal value corresponding to the timeindex value is calculated. The imaginary component is divided by thereal component to generate a quotient. An arctangent of the quotient iscalculated to generate a coarse carrier frequency offset estimate.

In other features of the invention, a system and method estimates finecarrier frequency offset in an orthogonal frequency divisionmultiplexing receiver of a wireless local area network. A symbol timingestimate is generated that identifies a start time of first and secondlong training symbols of a preamble of a data packet. The first andsecond long training symbols of the preamble are used to generate areceived signal. The first and second long training symbols arecorrelated to generate a correlation signal. A fine carrier frequencyoffset is calculated from the correlation signal.

In yet other features, the step of calculating includes calculatingimaginary and real components of the correlation signal. The imaginarycomponent is divided by the real component to generate a quotient. Anarctangent of the quotient is calculated to generate the fine carrierfrequency offset estimate.

In other features of the invention, a system and method updates channelestimates in an orthogonal frequency division multiplexing receiver of awireless local area network. The channel estimates are generated for anorthogonal frequency division multiplexing subcarrier as a function ofsubcarrier index values. A complex number is generated by summing aproduct of frequency domain signals and the channel estimates for eachof the subcarrier index values and dividing the sum by a sum of asquared absolute value of the channel estimate for each of thesubcarrier index values. The complex number is multiplied by the channelestimates to generate said updated channel estimates.

In still other features of the invention, a system and method adapt acarrier frequency offset estimate in an orthogonal frequency divisionmultiplexing receiver of a wireless local area network. Channelestimates are generated for an orthogonal frequency divisionmultiplexing subcarrier as a function of subcarrier index values. Acomplex number is generated by summing a product of frequency domainsignals and the channel estimates for each of the subcarrier indexvalues. The sum is divided by a sum of a squared absolute value of thechannel estimate for each of the subcarrier index values. An imaginarycomponent of the complex number is calculated.

In yet other features, the imaginary component is multiplied by anadaptation parameter to generate a product. The product is added to acarrier frequency offset estimate to produce an adapted carrierfrequency offset estimate.

Further areas of applicability of the present invention will becomeapparent from the detailed description provided hereinafter. It shouldbe understood that the detailed description and specific examples, whileindicating the preferred embodiment of the invention, are intended forpurposes of illustration only and are not intended to limit the scope ofthe invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 illustrates a preamble of a packet transmitted by an orthogonalfrequency division multiplexing receiver according to the prior art;

FIG. 2 is a functional block diagram of an OFDM transmitter according tothe present invention;

FIG. 3 is a functional block diagram of an OFDM receiver according tothe present invention;

FIG. 4 is a simplified functional block diagram of the OFDM receiver ofFIG. 3;

FIG. 5 is a graph illustrating M_(n) as a function of a time interval n;

FIG. 6 is an exemplary functional block diagram for calculating M_(n)and P_(n);

FIG. 7 is a flowchart illustrating steps for calculating symbol timing,carrier frequency offset and phase noise;

FIG. 8 is an exemplary functional block diagram for calculating updatedchannel estimates and an adapted carrier frequency estimate;

FIG. 9 is a flowchart illustrating steps for calculating the updatedchannel estimates; and

FIG. 10 is a flowchart illustrating steps for calculating the adaptedcarrier frequency estimate.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description of the preferred embodiment(s) is merelyexemplary in nature and is in no way intended to limit the invention,its application, or uses.

Referring now to FIG. 2, an OFDM transmitter 30 is shown. The OFDMtransmitter 30 includes a data scrambler 32 that receives input bits andscrambles the bits to prevent long strings of 1's and 0's. An output ofthe data scrambler 32 is input to a convolutional encoder 34 that addsredundant bits. For example, for each input bit the convolutionalencoder 34 may generate two output bits in a rate ½ convolutional coder.Skilled artisans can appreciate that other code rates may be employed.An output of the convolutional encoder 34 is input to an interleaver andsymbol mapper 36.

An output of the interleaver and symbol mapper 36 is input to a serialto parallel (S/P) converter 38. Outputs of the S/P converter 38 areinput to an inverse fast Fourier transform (FFT) circuit 40. Outputs ofthe inverse FFT circuit 40 are input to a parallel to serial (P/S)converter 42. An output of the P/S converter 42 is input to a cyclicprefix adder 44 that adds guard interval bits. An output of the cyclicprefix adder 44 is input to a waveform shaper 46. An output of thewaveform shaper 46 is input to a digital to analog (D/A) converter 48.An output of the D/A converter 48 is input to a radio frequency (R/F)amplifier 50 that is connected to an antenna 52. In a preferredembodiment, the OFDM transmitter 30 complies with IEEE section802.11(a).

Referring now to FIG. 3, an OFDM receiver 60 receives the RF signalsthat are generated by the OFDM transmitter 30. The receiver 60 includesantennas 62-1 and 62-2. A switch 64 selects one of the antennas 62 basedupon the strength of the RF signal detected by the antenna 62. Anamplifier 66 is connected to an output of the switch 64. An analog todigital (A/D) converter 68 is connected to an output of the amplifier66. An automatic gain control (AGC), antenna diversity and packetdetection circuit 70 is connected to an output of the A/D converter 68.When the gain of the AGC decreases, a packet is detected. A symboltiming and carrier frequency offset circuit 74 according to the presentinvention is connected to an output of the circuit 70. The symbol timingand carrier frequency offset circuit 74 identifies a carrier frequencyoffset ω_(Δ), a starting time n_(g) of a guard interval, and phase noiseas will be described more fully below. The circuit 74 typicallymultiples the samples by e^(−jω) _(Δ) ^(n) where n is a sample timeindex.

A cyclic prefix remover 76 is connected to an output of the symboltiming and carrier frequency offset circuit 74. A S/P converter 78 isconnected to an output of the cyclic prefix remover 76. A FFT circuit 80is connected to an output of the S/P converter 78. A P/S converter 82 isconnected to an output of the FFT circuit 80. A demap and deinterleavecircuit 84 is connected to an output of the P/S converter 82.

A channel estimator 86 that estimates multipath is connected to anoutput of the symbol timing and carrier frequency offset circuit 74. Afrequency equalizer (FEQ) 90 is connected to an output of the channelestimator 86. An output of the FEQ 90 is input to the demap anddeinterleave circuit 82. An output of the demap and deinterleave circuit82 is input to a sample recovery clock 94 and to a Viterbi decoder 96.An output of the sample recovery clock 94 is input to the A/D converter62. An output of the Viterbi decoder 96 is input to a descrambler 98.

Referring now to FIG. 4, a simplified functional block diagram of FIG. 3is shown and includes a radio frequency (RF) amplifier 100 thatamplifies the received RF signal. An output of the amplifier 100 isinput to a multiplier 102 having another input connected to a localoscillator (LO) 104. An output of the multiplier 102 is filtered by afilter 108 and input to an analog to digital (A/D) converter 110 havinga sampling rate of 1/T_(s). The A/D converter 110 generates samplesr_(n). A typical value for 1/T_(s) is 20 MHz, although other samplingfrequencies may be used. During the initial periods of the shorttraining symbol 12, the circuit 70 brings the signal within a dynamicrange of the OFDM receiver 60. Antenna selection for receive diversityis also performed.

After packet detection and AGC settling, the following quantities arecomputed for estimation of OFDM symbol timing:q _(n) =sgn[

(r _(n))]+jsgn[ℑ(r _(n))]

$P_{n\;} = {\sum\limits_{m = 1}^{L}\;{q_{n + m - {2L}}^{*}q_{n + m - L}}}$M _(n)=α_(s) M _(n−1)+(1−α_(s))(|

(P _(n))|+|ℑ(P _(n))|)

Where L=T_(short)/T_(s) is the number of samples in one short trainingsymbol,

is a real component of an argument, and ℑ is an imaginary component ofthe argument. A typical value for L is L=16, although other values maybe used. q_(n) contains sign bits of real and imaginary components ofthe received signal r_(n). Quantization simplifies the hardwareprocessing for symbol timing acquisition. P_(n) represents a correlationbetween two adjacent short training symbols of q_(n). M_(n) represents afiltered version of |

(P_(n))|+|ℑ(P_(n))|. The filter is preferably a single pole filter witha pole α_(s). A typical value of α_(s) is α_(s)=1−3/32, although othervalues may be used.

Referring now to FIG. 5, a plot of M_(n) for a multipath channel havinga delay spread of 50 ns is shown. M_(n) has a plateau at 120 thatresults from the periodicity of the channel output due to the repetitionof the short training symbols. The duration of the plateau depends onthe number of periods of the short training symbol that remain afterantenna selection and AGC settling. Therefore, a center of the plateauis not the best symbol timing estimate. A falling edge of the plateauindicates that no more short training symbols are present and that M_(n)includes samples from the guard interval 14 that precedes the longtraining symbols 16. Therefore, the falling edge of the plateau providesan estimate of the symbol timing.

After AGC settling, P_(n) and M_(n) are calculated. A left edge n₁ ofthe plateau 120 is defined by M_(n)>τ₁A. Typical values for τ₁ and A areτ₁=0.7 and A=32/(T_(s)▪20 MHz). A maximum value of M_(n) is updated andstored as M_(n,max) as time progresses. The complex number P_(n)corresponding to M_(n,max) is denoted by P_(n,max), which is alsoupdated and stored as time progresses. A local maximum valueM_(n,localmax), is set equal to M_(n−1) if the following conditions aremet: M_(n−1)≧M_(n−2) and M_(n−1)>M_(n). The local maximum valueM_(n,localmax) is updated and stored as time progresses.

A time index n_(g) is set to n−1 if the following conditions are met:M_(n)<τ₂ M_(n,localmax) and M_(n−1)≧τ₂ M_(n,localmax). The index n_(g)is used to determine the symbol timing. A typical value for τ₂ isτ₂=0.9. To determine a right edge n_(r) of the plateau 120, M_(n) muststay below τ₁M_(n,max) for at least B consecutive samples. A typicalvalue for B is B=8/(T_(s)▪20 MHz). Once n_(r) is determined, the coarsefrequency offset ω_(Δ) is determined by:ω_(Δ)=tan⁻¹[ℑ(P _(n,max))/

(P _(n,max))]/(L)A coarse frequency correction e^(−jω) _(Δ) ^(n) is applied to thereceived signal. The symbol timing is then estimated byn_(g)′=n_(g)−n_(Δ). A typical value for n_(Δ) is n_(Δ)=32.

Referring now to FIGS. 6 and 7, an exemplary implementation of thecoarse frequency and symbol timing circuit 70 is shown. Typicalparameter values include L=32, τ₁=0.7, A=64, τ₂=0.7, B=15, n_(Δ)=25,T_(s)=40 MHz, and α_(s)=1−3/32. A low pass filter (LPF) 150 is connectedto a sign-bit quantizer 152. The sign-bit quantizer 152 is connected toa buffer 154 and a multiplier 156. An L-1 output of the buffer 154 isconnected to a conjugator 158 and a multiplier 160. A 2L-1 output of thebuffer 154 is connected to a conjugator 162, which has an outputconnected to the multiplier 160. An output of the multiplier 160 isconnected to an inverting input of an adder 164. An output of themultiplier 156 is connected to a non-inverting input of the adder 164.An output of the adder 164 is input to an adder 170. An output of theadder 170 is equal to P_(n) and is connected to a delay element 172 thatis fed back to an input of the adder 170. The output of the adder 174 isalso input to a metric calculator 174.

An output of the metric calculator 174 is connected to a multiplier 176.Another input of the multiplier is connected to a signal equal to1−α_(s). An output of the multiplier is input to an adder 180. An outputof the adder 180 is equal to M_(n) and is connected to a delay element182, which has an output that is connected to a multiplier 184. Themultiplier 184 has another input connected to α_(s). An output of themultiplier 184 is connected to an input of the adder 180.

Referring now to FIG. 7, steps performed by the coarse frequency circuitand symbol timing circuit 74 is shown generally at 200. Control beginsin step 202. In step 204, M_(nmax), M_(nlocalmax), n₁, n_(r), n_(s),n_(g), n_(max), and ctr are initialized. In step 204, control determineswhether n₁=0 and M_(n)>τ₁A. If true, control sets n₁=n in step 208 andcontinues with step 210. If false, control determines whetherM_(n)>M_(nmax). If true, control continues with step 212 where controlsets M_(nmax)=M_(n) and nmax=n and then continues with step 214. Iffalse, control continues with step 214 where control determines whetherboth M_(n−1)>M_(n−2) and M_(n−1)>M_(n).

If true, control sets M_(nlocalmax)=M_(n−1) and then continues with step218. If false, control determines whether M_(n)<τ₂M_(nlocalmax) andM_(n−1)≧τ₂ M_(nlocalmax) in step 218. If true, control sets n_(g)=n−1 instep 220 and continues with step 224. If false, control determineswhether n₁>0 and M_(n−1)>τ₁M_(nmax) in step 224. If true, control setsctr=0 in step 226 and continues with step 230. If false, controldetermines whether n₁>0 in step 232. If true, control sets ctr=ctr+1 instep 234 and continues with step 230. In step 230, control determineswhether ctr=B or n=10L-1. If false, control sets n=n+1 in step 234 andreturns to step 206. If true, control sets n_(r)=n−B in step 238. Instep 240, control calculates ω_(Δ)=tan⁻¹[Im(P_(nmax))/Re(P_(nmax))]/(L)and ρ=(1−ω_(Δ)/ω_(carrier)). In step 242, control estimates a start oflong training symbol using n_(g)′=n_(g)−n_(Δ).

IEEE section 802.11(a) specifies that the transmit carrier frequency andsampling clock frequency are derived from the same reference oscillator.The normalized carrier frequency offset and the sampling frequencyoffset are approximately equal. Since carrier frequency acquisition isusually easier than sampling period acquisition, sampling clock recoveryis achieved using the estimate of the carrier frequency offset ω_(Δ).

The coarse frequency estimate ω_(Δ) is used to correct all subsequentreceived samples. The coarse frequency estimate ω_(Δ) is refined duringthe long training symbols specified in IEEE section 802.11(a). r_(0,n),and r_(1,n) (n=0, . . . , N−1) are the received samples that areassociated with the long training symbols 16-1 and 16-2 (or L0 and L1),respectively. The value N is the number of samples contained within eachlong training symbol 16. A typical value for N is N=64 (for 1/T_(s)=20MHz) (where L=16 and n_(Δ)=32). The estimate of fine frequency offsetω_(Δ,fine) is obtained by:ω_(Δ,fine)=tan⁻¹[ℑ(C _(L))/

(C _(L))]where

$C_{L} = {\sum\limits_{n = 1}^{N - 1}\;{r_{0,n}^{*}r_{1,n}}}$The sampling clock is also updated accordingly.

The residual frequency offset and phase noise are tracked during thedata portion of the OFDM packet. Ĥ_(k) are channel estimates for theOFDM subcarriers as a function of the subcarrier index k. The channelestimates Ĥ_(k) are multiplied by a complex number Ĉ_(ML) to compensatefor common amplitude and phase error due to the residual frequencyoffsets and phase noise. P_(k), kεK, are received frequency domainsignals on the pilot tones after the known BPSK modulation is removed,where K={−21, −7, 7, 21}. The pilot tones are used to derive a maximumlikelihood estimate of Ĉ_(ML):

${\hat{C}}_{M\; L} = \frac{\sum\limits_{k\;\varepsilon\; K}\;{{\hat{H}}_{k}^{*}P_{k}}}{\sum\limits_{k\;\varepsilon\; K}\;{{\hat{H}}_{k}}^{2}}$The new channel estimates are then {tilde over (H)}_(k)=Ĉ_(ML)Ĥ_(k).These updated channel estimates are used in the frequency equalizer(FEQ) for data detection.

The carrier frequency estimate ω_(Δ) is adapted by:ω_(Δ) ^(l)=ω_(Δ) ^(l-1)+βℑ(Ĉ_(ML))where β is an adaptation parameter and the subscript 1 represents valuesduring the 1-th OPDM data symbol. A typical value of β is β=1/1024. Thesampling clock frequency is also adapted accordingly.

Since the guard interval 14 of an OFDM data symbol is longer than thechannel impulse response, an additional tolerance factor is provided inthe symbol timing estimate. In order to obtain a symbol timing estimatewithin an acceptable range, a modified symbol timing estimate n_(g)′ isgenerated. The modified symbol timing estimate n_(g)′ is equal ton_(g)−n_(Δ) where n_(Δ). A typical value for n_(Δ) is n_(Δ)=32 whenL=16.

Referring now to FIG. 8, an exemplary circuit 250 for calculating theupdated channel estimates and the adapted carrier frequency estimateω_(Δ) is shown. The circuit includes multipliers 256-1, 256-2, . . . ,256-n that multiply Ĥ*_(k) and P_(k), for kεK. Absolute value circuits260-1, 260-2, . . . 260-n calculate an absolute value of Ĥ_(k). Outputsof the absolute value circuit 260 are squared by multipliers 264-1,264-2, . . . , 264-n. Outputs of the multipliers 256 are input to anadder 266. Outputs of the multipliers 264 are input to an adder 270. Anoutput of the adder 266 is input to a numerator input of a divider 272.An output of the adder 270 is input to a denominator input of thedivider 272. An output of the divider 272 Ĉ_(ML) is input to amultiplier 274. Another input of the multiplier 274 is connected toĤ_(k). An output of the multiplier 274 generates {tilde over (H)}_(k).

An output of the divider 272 is input to an imaginary component circuit280 that outputs an imaginary component of Ĉ_(ML). An output of theimaginary component circuit 280 is input to a multiplier 284. Anotherinput of the multiplier is connected to the adaptation parameter β. Anoutput of the multiplier 284 is input to an adder 286. Another input ofthe adder is connected to ω_(Δ) ^(l-1). An output of the adder 286generates ω_(Δ) ^(l) which is the adapted carrier frequency estimate.

Referring now to FIG. 9, steps for calculating new channel estimates areshown generally at 300. In step 302, control begins. In step 304,channel estimates Ĥ_(k) are obtained. In step 306, frequency domainsignals P_(k) on the pilot tones are obtained after BPSK modulation isremoved. In step 308, the conjugates of the channel estimates Ĥ_(k) aremultiplied by the frequency domain signals P_(k) and summed for eachvalue of K. In step 310, Ĉ_(ML) is computed by dividing the summedproduct generated in step 308 and divided by the sum for each value of kof the squared absolute values of Ĥ_(k). In step 312, the channelestimates Ĥ_(k) are multiplied by Ĉ_(ML) to obtain new channel estimates{tilde over (H)}_(k). Control ends in step 314.

Referring now to FIG. 10, steps for generating the adapted carrierfrequency estimate are shown generally at 320. Control begins in step322. In step 324, the imaginary component of Ĉ_(ML) is generated. Instep 326, the imaginary component of Ĉ_(ML) is multiplied by theadaptation parameter β. In step 328, the product of step 326 is added toω_(Δ) ^(l-1) (the l-1th carrier frequency offset estimate) to generateω_(Δ) ^(l). Control ends in step 330.

In an alternate method for calculating coarse frequency according to thepresent invention, after packet detection and AGC settling, thefollowing quantities are computed for estimation of OFDM symbol timing:

${P_{n} = {\sum\limits_{m = 1}^{L}{r_{n + m - {2L}}^{*}r_{n + m - L}}}}\;$

${R_{n} = {\sum\limits_{m = 1}^{L}{r_{n + m - L}}^{2}}}\;$M _(n) =|P _(n)|² /R _(n) ²

Where L=T_(short)/T_(s) is the number of samples in one short trainingsymbol. A typical value for L=16, although other values may be used.P_(n) represents a correlation between two adjacent short trainingsymbols. R_(n) represents an average received power in a short trainingsymbol. M_(n) represents a normalized correlation between two adjacentshort training symbols.

M_(n) exhibits the plateau at 120 due to the repetition of the shorttraining symbol. In other words, M_(n) is a maximum value as a samplewindow moves across the short training symbols 12 after packet detectionand AGC settling. P_(n) correlates received signals for two adjacentshort training samples. Preferably, the sampling window has a durationof 2L, although other durations are contemplated.

The duration of the plateau 120 depends upon the number of periods ofthe short training symbol that remain after antenna selection and AGCsettling is complete. Therefore, the center of the plateau 120 of M_(n)is not usually the best symbol timing estimate. The right edge of theplateau 120 indicates that no more short training symbols are present.Samples that occur after the right edge of the plateau include samplesfrom the guard interval 14 that precedes the long training symbols 16.Therefore, the right edge of the plateau 120 provides a good estimate ofthe symbol timing.

After packet detection and AGC settling, M_(n) is computed. M_(max) isthe maximum of M_(n) and n_(max) corresponds to a time index at whichM_(max) occurs. Points n₁ and n_(r) are left and right edges of theplateau 120, respectively. The points n₁ and n_(r) are identified suchthat M_(n1)≈M_(nr)≈τ₁M_(max) and n₁<n_(max)<n_(r). In other words, n₁and n_(r) are the points preceding and following the maximum of M_(n)that are equal to a threshold τ₁ multiplied by M_(max). A typical valuefor τ₁ is 0.7. The center of the plateau 120 is estimated by themidpoints n_(c)=(n_(r)+n₁)/2.

The carrier frequency offset Δf is estimated by:α=tan⁻¹[ℑ(P _(nc))/

(P _(nc))]Δf=α/(2πT _(short)) which is valid if |Δf|<1/(2T _(short)).For example, |Δf|<1/(2T_(short))=625 kHz for T_(short)=0.8 μs. Theestimate of the carrier frequency offset Δf may be refined using acorrelation of the two long training symbols after the sample timing isdetermined as will be described below.

In order to detect the falling edge of the plateau of M_(n), the meanabsolute difference of M_(n) near the center of the plateau is computed:

$D_{K} = {\left( {1/K} \right){\sum\limits_{n = {n_{c} - {({K/2})} + 1}}^{n_{c} + {({K/2})}}\;{{M_{n} - M_{n - 1}}}}}$Where K is the number of terms in the estimate of the mean absolutedifference. A typical value for K is (n_(r)−n₁)/2. The sample indexn_(g) at the beginning of the guard interval 14 preceding the longtraining symbols 16 is estimated by detecting the right or followingedge of the plateau of M_(n). In other words, n_(g) satisfies thefollowing conditions:n_(g)>n_(c)M _(n) _(g) <M _(n) _(g) ⁻¹|M _(n) _(g) −M _(n) _(g−1) |>τ₂ D _(K)n _(g) ′=n _(g) −nΔA typical value for τ₂ is 10.

Since the guard interval 14 of an OFDM data symbol is longer than thechannel impulse response, an additional tolerance factor is provided inthe symbol timing estimate. In order to obtain a symbol timing estimatewithin an acceptable range, a modified symbol timing estimate n_(g)′ isgenerated. The modified symbol timing estimate n_(g)′ is equal ton_(g)−n_(Δ) where n_(Δ) is a small number that is less than the numberof samples in the guard interval for a data symbol. For IEEE 802.11(a),the number of samples in the guard interval for a data symbol is L,which is the number of samples in a short training symbol. For example,a typical value for n_(Δ) is L/4.

The identification of the precise time that M_(n) decreases from theplateau 120 (e.g. when the short training symbols 12 end) may varysomewhat. To accommodate the possible variation, the modified symboltiming estimate n_(g)′ provides additional tolerance. With the modifiedsymbol timing estimate n_(g)′, a sampling window begins earlier in theguard interval 14.

IEEE section 802.11(a) specifies that the transmit frequency and sampleclock frequency are derived from the same reference oscillator.Therefore, the normalized carrier frequency offset and sampling periodoffset are approximately equal. Since carrier frequency acquisition ismore simple than sampling period acquisition, sampling clock recovery isachieved using the estimate of the carrier frequency offset.

The initial carrier frequency offset estimate Δf₀ is obtained during theshort timing symbols 12 in the preamble 10 of each packet as previouslydescribed above. Each complex output sample of the A/D converter 68 isadjusted using a current carrier frequency offset estimate Δf. If theoriginal sampling period (before acquisition) is equal to T^(orig), thefirst update of the sampling period is:T ₀ =T ^(orgi)(1−(Δf ₀ /f _(nominal))).Where f_(nominal) is the nominal carrier frequency. The estimate of thecarrier frequency offset during the long training symbols 16 is used toobtain Δf₁=Δf₀+ε₁. The corresponding update of the sampling period is:T ₁ =T ₀(1−(ε₁ /f _(nominal)))

During the OFDM data symbols that occur after the long training symbols16, four subcarriers are used for pilot tones. After removing the knownbinary phase shift key (BPSK) modulation of the pilot tones, the mainphase of the 4 pilots is determined to estimate a residual carrierfrequency offset, ε_(n), where n is the index of the OFDM symbol. Foreach OFDM symbol, the update of the carrier frequency offset and thesampling period is given by:Δf _(n) =Δf _(n−1)+βε_(n)T _(n) =T _(n−1)(1−(βε_(n) /f _(nominal)))Where β is a loop parameter. This method is currently being used with azero order hold after IFFT in the transmitter 30 (to model D/A).

Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the present invention can beimplemented in a variety of forms. Therefore, while this invention hasbeen described in connection with particular examples thereof, the truescope of the invention should not be so limited since othermodifications will become apparent to the skilled practitioner upon astudy of the drawings, the specification and the following claims.

1. A method for estimating carrier frequency offset in an orthogonalfrequency division multiplexing receiver of a wireless local areanetwork, comprising: receiving a preamble including at least twoadjacent short training symbols; sampling said at least two adjacentshort training symbols of said preamble at a first rate; and correlatingsaid at least two adjacent short training symbols to generate acorrelation signal.
 2. The method of claim 1 further comprisingnormalizing said correlation signal to generate a normalized correlationsignal.
 3. The method of claim 2 wherein said normalizing step furthercomprises dividing said correlation signal by an energy of at least oneof said adjacent short training symbols.
 4. The method of claim 2further comprising: repeating said sampling, correlating and normalizingsteps for all of said short training symbols; and identifying a maximumvalue of said normalized correlation signal during said short trainingsymbols.
 5. The method of claim 4 further comprising multiplying saidmaximum value of said normalized correlation signal by a threshold valueto identify left and right edges of a plateau defined by said normalizedcorrelation signal.
 6. The method of claim 5 wherein said thresholdvalue is greater than zero and less than one.
 7. The method of claim 5further comprising identifying left and right time index valuescorresponding to said left and right edges.
 8. The method of claim 7further comprising identifying a center time index value using said leftand right time index values.
 9. The method of claim 8 further comprisingusing said center time index value and a correlation value correspondingto said center time index value to calculate said carrier frequencyoffset.
 10. The method of claim 9 further comprising: calculating afirst value by dividing an imaginary component of said correlation valueat said center time index value by a real component of said correlationvalue at said center time index value; and calculating an arctangent ofsaid first value.
 11. The method of claim 1 wherein said method is asoftware method.
 12. The method of claim 10 further comprisingcalculating said carrier frequency offset by dividing said arctangent by2πT_(short) wherein T_(short) is the period of said short trainingsymbols.
 13. The method of claim 1 wherein said preamble forms part ofan orthogonal frequency division multiplex (OFDM) packet.
 14. A methodfor estimating carrier frequency offset in an orthogonal frequencydivision multiplexing receiver of a wireless local area network,comprising: receiving a preamble including a plurality of short trainingsymbols; sampling said short training symbols of said preamble using asampling window; and correlating samples from the short training symbolsin a first half of said sampling window with samples from the shorttraining symbols in a second half of said sampling window to generate acorrelation signal.
 15. The method of claim 14 wherein said samplingwindow has a period that is equal to a duration of two short trainingsymbols.
 16. The method of claim 14 further comprising normalizing saidcorrelation signal to generate a normalized correlation signal.
 17. Themethod of claim 14 wherein said method is a software method.
 18. Themethod of claim 14 wherein said preamble forms part of an orthogonalfrequency division multiplex (OFDM) packet.
 19. A method for estimatingcarrier frequency offset in an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising:receiving a preamble including a plurality of short training symbols;sampling said short training symbols of said preamble using a samplingwindow; correlating a first half of said sampling window with a secondhalf of said sampling window to generate a correlation signal;normalizing said correlation signal to generate a normalized correlationsignal; and wherein said normalizing step further comprises dividingsaid correlation signal by an energy of at least one of said first andsecond halves of said sampling window.
 20. The method of claim 19further comprising repeating said sampling, correlating and normalizingsteps for all of said short training symbols.
 21. The method of claim 20further comprising identifying a maximum value of said normalizedcorrelation signal during said short training symbols.
 22. The method ofclaim 21 further comprising multiplying said maximum value of saidnormalized correlation signal by a threshold value to identify left andright edges of a plateau defined by said normalized correlation signal.23. The method of claim 22 wherein said threshold value is greater thanzero and less than one.
 24. The method of claim 22 further comprisingidentifying left and right time index values corresponding to said leftand right edges.
 25. The method of claim 24 further comprisingidentifying a center time index value using said left and right timeindex values.
 26. The method of claim 25 further comprising using saidcenter time index value and a correlation value corresponding to saidcenter time index value to calculate said carrier frequency offset. 27.The method of claim 26 further comprising calculating a first value bydividing an imaginary component of said correlation value at said centertime index value by a real component of said correlation value at saidcenter time index value and calculating an arctangent of said firstvalue.
 28. The method of claim 27 further comprising calculating saidcarrier frequency offset by dividing said arctangent by 2πT_(short)wherein T_(short) is the period of said short training symbols.
 29. Amethod for estimating carrier frequency offset in an orthogonalfrequency division multiplexing receiver of a wireless local areanetwork, comprising: sampling at least two adjacent short trainingsymbols of a preamble of a data packet to generate a received signal;quantizing sign bits of real and imaginary components of said receivedsignal; and correlating said quantized sign bits to generate acorrelation signal.
 30. The method of claim 29 further comprisinggenerating a filtered sum of an absolute value of a real component ofsaid correlation signal and an absolute value of an imaginary componentof said correlation signal.
 31. The method of claim 30 wherein saidfiltered sum is generated by a single pole filter.
 32. The method ofclaim 30 further comprising identifying a local maximum value of saidfiltered sum during said short training symbols.
 33. The method of claim32 wherein said local maximum value is identified by updating andstoring said filtered sums and by comparing at least one filtered sum toa prior filtered sum and to a subsequent filtered sum.
 34. The method ofclaim 29 wherein said method is a software method.
 35. The method ofclaim 30 further comprising identifying a maximum value of said filteredsum during said short training symbols.
 36. The method of claim 35further comprising identifying said maximum value by updating andstoring said filtered sums and by comparing at least one filtered sum toa prior filtered sum and to a subsequent filtered sum.
 37. The method ofclaim 36 further comprising: identifying a time index valuecorresponding to said maximum value; and identifying a correlationsignal value corresponding to said time index value.
 38. The method ofclaim 37 further comprising: calculating an imaginary component of saidcorrelation signal value corresponding to said time index value;calculating a real component of said correlation signal valuecorresponding to said time index value; dividing said imaginarycomponent by said real component to generate a quotient; and calculatingan arctangent of said quotient to generate a coarse carrier frequencyoffset estimate.
 39. The method of claim 38 further comprising:multiplying said received signal by e^(−jnω) ^(Δ) where ω_(Δ) is saidcoarse carrier frequency offset estimate and n is a time index.
 40. Amethod for estimating carrier frequency offset in an orthogonalfrequency division multiplexing receiver of a wireless local areanetwork, comprising: sampling short training symbols of a preamble of adata packet to generate a received signal; quantizing sign bits of realand imaginary components of said received signal; generating a filteredsum of an absolute value of a real component of said correlation signaland an absolute value of an imaginary component of said correlationsignal; identifying a local maximum value of said filtered sum duringsaid short training symbols; and multiplying said local maximum value ofsaid filtered sum by a threshold value to identify a right edge of aplateau wherein said threshold value is greater than zero and less thanone.
 41. The method of claim 40 further comprising: identifying a righttime index value corresponding to said right edge; and calculatingsymbol timing from said right time index value.
 42. A method forestimating carrier frequency offset in an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising:sampling short and long training symbols of a preamble of a data packetto generate a received signal; quantizing sign bits of real andimaginary components of said received signal; correlating said quantizedsign bits of at least two adjacent short training symbols to generate afirst correlation signal; generating a symbol timing estimate that isbased on said first correlation signal and identifies a start time offirst and second ones of said long training symbols correlating saidfirst and second long training symbols to generate a second correlationsignal; and calculating a fine carrier frequency offset from said secondcorrelation signal.
 43. The method of claim 42 wherein said step ofcalculating further comprises: calculating an imaginary component ofsaid correlation signal; calculating a real component of saidcorrelation signal; dividing said imaginary component by said realcomponent to generate a quotient; and calculating an arctangent of saidquotient to generate said fine carrier frequency offset estimate. 44.The method of claim 43 further comprising updating a sampling clock withsaid fine carrier frequency offset estimate.
 45. A method for adapting acarrier frequency offset estimate in an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising:generating channel estimates for an orthogonal frequency divisionmultiplexing subcarrier as a function of subcarrier index values duringa data portion of an orthogonal frequency division multiplexing packet;generating a complex number by summing a product of frequency domainsignals and said channel estimates for each of said subcarrier indexvalues and dividing said sum by a sum of a squared absolute value ofsaid channel estimate for each of said subcarrier index values;calculating an imaginary component of said complex number; and adaptingthe carrier frequency offset estimate based on said imaginary component.46. A method for adapting a carrier frequency offset estimate in anorthogonal frequency division multiplexing receiver of a wireless localarea network, comprising: generating channel estimates for an orthogonalfrequency division multiplexing subcarrier as a function of subcarrierindex values; generating a complex number by summing a product offrequency domain signals and said channel estimates for each of saidsubcarrier index values and dividing said sum by a sum of a squaredabsolute value of said channel estimate for each of said subcarrierindex values; calculating an imaginary component of said complex number;multiplying said imaginary component by an adaptation parameter togenerate a product; and adding said product to a prior carrier frequencyoffset estimate to produce an adapted carrier frequency offset estimate.47. A carrier frequency offset estimator for an orthogonal frequencydivision multiplexing receiver of a wireless local area network,comprising: sampling means for sampling at least two adjacent shorttraining symbols of a preamble of a data packet to generate a receivedsignal; quantizing means for quantizing sign bits of real and imaginarycomponents of said received signal; and correlating means forcorrelating said quantized sign bits of at least two adjacent shorttraining symbols to generate a correlation signal.
 48. The carrierfrequency offset estimator of claim 47 further comprising filtered sumgenerating means for generating a filtered sum of an absolute value of areal component of said correlation signal and an absolute value of animaginary component of said correlation signal.
 49. The carrierfrequency offset estimator of claim 48 wherein said filtered sum isgenerated by a single pole filter.
 50. The carrier frequency offsetestimator of claim 48 further comprising first identifying means foridentifying a local maximum value of said filtered sum during said shorttraining symbols.
 51. The carrier frequency offset estimator of claim 50wherein said local maximum value is identified by updating and storingsaid filtered sums and by comparing at least one filtered sum to a priorfiltered sum and to a subsequent filtered sum.
 52. The carrier frequencyoffset estimator of claim 50 further comprising first multiplying meansfor multiplying said local maximum value of said filtered sum by athreshold value to identify a right edge of a plateau.
 53. The carrierfrequency offset estimator of claim 52 wherein said threshold value isgreater than zero and less than one.
 54. The carrier frequency offsetestimator of claim 52 further comprising: second identifying means foridentifying a right time index value corresponding to said right edge;and first calculating means for calculating symbol timing from saidright time index value.
 55. The carrier frequency offset estimator ofclaim 48 further comprising third identifying means for identifying amaximum value of said filtered sum during said short training symbols.56. The carrier frequency offset estimator of claim 55 furthercomprising fourth identifying means for identifying said maximum valueby updating and storing said filtered sums and by comparing at least onefiltered sum to a prior filtered sum and to a subsequent filtered sum.57. The carrier frequency offset estimator of claim 56 furthercomprising: fifth identifying means for identifying a time index valuecorresponding to said maximum value; and sixth identifying means foridentifying a correlation signal value corresponding to said time indexvalue.
 58. The carrier frequency offset estimator of claim 57 furthercomprising: second calculating means for calculating an imaginarycomponent of said correlation signal value corresponding to said timeindex value; third calculating means for calculating a real component ofsaid correlation signal value corresponding to said time index value;dividing means for dividing said imaginary component by said realcomponent to generate a quotient; and fourth calculating means forcalculating an arctangent of said quotient to generate a coarse carrierfrequency offset estimate.
 59. The carrier frequency offset estimator ofclaim 58 further comprising: second multiplying means for multiplyingsaid received signal by e^(−jnω) ^(Δ) where ωΔ is said coarse carrierfrequency offset estimate and n is a time index.
 60. A carrier frequencyoffset estimator for an orthogonal frequency division multiplexingreceiver of a wireless local area network, comprising: sampling meansfor sampling short and long training symbols of a preamble of a datapacket to generate a received signal; quantizing means for quantizingsign bits of real and imaginary components of said received signal;first correlating means for correlating said quantized sign bits of atleast two adjacent short training symbols to generate a firstcorrelation signal; symbol timing generating means for generating asymbol timing estimate that is based on said first correlation signaland identifies a start time of first and second ones of said longtraining correlating means for correlating said first and second longtraining symbols to generate a second correlation signal; and firstcalculating means for calculating a fine carrier frequency offset fromsaid second correlation signal.
 61. The carrier frequency offsetestimator of claim 60 wherein said first calculating means calculates animaginary component of said correlation signal, calculates a realcomponent of said correlation signal, divides said imaginary componentby said real component to generate a quotient, and calculates anarctangent of said quotient to generate said fine carrier frequencyoffset estimate.
 62. The carrier frequency offset estimator of claim 61further comprising updating means for updating a sampling clock withsaid fine carrier frequency offset estimate.
 63. A carrier frequencyoffset estimate adaptor for an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising:channel estimate generating means for generating channel estimates foran orthogonal frequency division multiplexing subcarrier as a functionof subcarrier index values during a data portion of an orthogonalfrequency division multiplexing packet; complex number generating meansfor generating a complex number by summing a product of frequency domainsignals and said channel estimates for each of said subcarrier indexvalues and dividing said sum by a sum of a squared absolute value ofsaid channel estimate for each of said subcarrier index values; firstcalculating means for calculating an imaginary component of said complexnumber; adapting means for adapting the carrier frequency offsetestimate based on said imaginary component.
 64. A carrier frequencyoffset estimate adaptor for an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising:channel estimate generating means for generating channel estimates foran orthogonal frequency division multiplexing subcarrier as a functionof subcarrier index values; complex number generating means forgenerating a complex number by summing a product of frequency domainsignals and said channel estimates for each of said subcarrier indexvalues and dividing said sum by a sum of a squared absolute value ofsaid channel estimate for each of said subcarrier index values; firstcalculating means for calculating an imaginary component of said complexnumber; and first multiplying means for multiplying said imaginarycomponent by an adaptation parameter to generate a product.
 65. Thecarrier frequency offset estimate adaptor of claim 64 further comprisingfirst adding means for adding said product to a prior carrier frequencyoffset estimate to produce an adapted carrier frequency offset estimate.66. A carrier frequency offset estimator for an orthogonal frequencydivision multiplexing receiver of a wireless local area network,comprising: a sampler that samples at least two adjacent short trainingsymbols of a preamble of a data packet to generate a received signal; aquantizer that quantizes sign bits of real and imaginary components ofsaid received signal; and a correlator that correlates said quantizedsign bits to generate a correlation signal.
 67. The carrier frequencyoffset estimator of claim 66 further a filtered sum generator thatgenerates a filtered sum of an absolute value of a real component ofsaid correlation signal and an absolute value of an imaginary componentof said correlation signal.
 68. The carrier frequency offset estimatorof claim 67 wherein said filtered sum is generated by a single polefilter.
 69. The carrier frequency offset estimator of claim 67 furthercomprising a first identifier circuit that identifies a local maximumvalue of said filtered sum during said short training symbols.
 70. Thecarrier frequency offset estimator of claim 69 wherein said localmaximum value is identified by updating and storing said filtered sumsand by comparing at least one filtered sum to a prior filtered sum andto a subsequent filtered sum.
 71. The carrier frequency offset estimatorof claim 69 further comprising a first multiplier circuit thatmultiplies said local maximum value of said filtered sum by a thresholdvalue to identify a right edge of a plateau.
 72. The carrier frequencyoffset estimator of claim 71 wherein said threshold value is greaterthan zero and less than one.
 73. The carrier frequency offset estimatorof claim 71 further comprising: second identifier circuit thatidentifies a right time index value corresponding to said right edge;and a first calculator that calculates symbol timing from said righttime index value.
 74. The carrier frequency offset estimator of claim 67further comprising a third identifier that identifies a maximum value ofsaid filtered sum during said short training symbols.
 75. The carrierfrequency offset estimator of claim 74 further comprising fourthidentifying means for identifying said maximum value by updating andstoring said filtered sums and by comparing at least one filtered sum toa prior filtered sum and to a subsequent filtered sum.
 76. The carrierfrequency offset estimator of claim 75 further comprising: a fifthidentifier that identifies a time index value corresponding to saidmaximum value; and a sixth identifier that identifies a correlationsignal value corresponding to said time index value.
 77. The carrierfrequency offset estimator of claim 76 further comprising: a secondcalculator that calculates an imaginary component of said correlationsignal value corresponding to said time index value; a third calculatorthat calculates a real component of said correlation signal valuecorresponding to said time index value; a divider that divides saidimaginary component by said real component to generate a quotient; and afourth calculator that calculates an arctangent of said quotient togenerate a coarse carrier frequency offset estimate.
 78. The carrierfrequency offset estimator of claim 77 further comprising: a secondmultiplier that multiplies said received signal by e^(−jnω) ^(Δ) whereω_(Δ) is said coarse carrier frequency offset estimate and n is a timeindex.
 79. A carrier frequency offset estimator for an orthogonalfrequency division multiplexing receiver of a wireless local areanetwork, comprising: a sampler that samples short and long trainingsymbols of a preamble of a data packet and generates a received signal;a quantizer that quantizes sign bits of real and imaginary components ofsaid received signal; a first correlator that correlates said quantizedsign bits of at least two adjacent short training symbols to generate afirst correlation signal; a symbol timing generator that produces asymbol timing estimate that is based on said first correlation signaland identifies a start time of first and second ones of said longtraining symbols; a second correlator that correlates said first andsecond long training symbols to generate a second correlation signal;and a first calculator that calculates a fine carrier frequency offsetfrom said second correlation signal.
 80. The carrier frequency offsetestimator of claim 79 wherein said first calculator calculates animaginary component of said correlation signal, calculates a realcomponent of said correlation signal, divides said imaginary componentby said real component to generate a quotient, and calculates anarctangent of said quotient to generate said fine carrier frequencyoffset estimate.
 81. The carrier frequency offset estimator of claim 80further comprising a sampling clock updater that updates a samplingclock with said fine carrier frequency offset estimate.
 82. A carrierfrequency offset estimate adaptor for an orthogonal frequency divisionmultiplexing receiver of a wireless local area network, comprising: achannel estimator that generates channel estimates for an orthogonalfrequency division multiplexing subcarrier as a function of subcarrierindex values during a data portion of an orthogonal frequency divisionmultiplexing packet; a complex number generator that generates a complexnumber by summing a product of frequency domain signals and said channelestimates for each of said subcarrier index values and dividing said sumby a sum of a squared absolute value of said channel estimate for eachof said subcarrier index values; a first calculator that calculates animaginary component of said complex number; and an adaptor that adaptsthe carrier frequency offset estimate based on said imaginary component.83. The carrier frequency offset estimate adaptor of claim 82 furthercomprising a first multiplier that multiplies said imaginary componentby an adaptation parameter to generate a product.
 84. The carrierfrequency offset estimate adaptor of claim 83 further comprising a firstadder that adds said product to a prior carrier frequency offsetestimate to produce an adapted carrier frequency offset estimate.